---
tag: 0W4RPA8QH3
kind: definition
name: Disjoint sets
msc: ["03E20"]
defines: 0XZ37KAB1Z
uses: [0HBRW4E6G1, 0ECVK59Y03]
sources:
  - url: https://en.wikipedia.org/wiki/Disjoint_sets
    locator: lead section
---

## Definition

Let $A$ and $B$ be [[sets|0SJ3RX9TXA]].
The sets $A$ and $B$ are disjoint when $A \cap B = \varnothing$.
A family of sets $(A_i)_{i \in I}$ is pairwise disjoint when $A_i \cap A_j = \varnothing$ for all $i, j \in I$ with $i \neq j$.

## Remarks

Example: $\{1, 2\}$ and $\{3, 4\}$ are disjoint, but $\{1, 2\}$ and $\{2, 3\}$ are not.
The blocks of a [[partition|09CCE86A6D]] are pairwise disjoint.
For finite disjoint sets, the number of elements of $A \cup B$ is the sum of the numbers of elements of $A$ and $B$.

## Explanations

### L1 human

Disjoint sets do not overlap.
The even integers and the odd integers are disjoint, because no integer is both.